12 



Just as tlie cont<?iits of a crop or of a class may be taken as the 

 product of the number of stems and the contents of the avei'age 

 tree, so we may also express it either as the sum of the basal areas 

 of all the stems (J) X the average height of the crop (H) % the 

 average form-factor {F) or as J x the average n'c^^-height {Ilr)- 

 We have thus three formulae — 

 (i), C ^ c n ... Valuation by means of the average tree. 

 {ii),^C = A SF... „ „ average form-factor. 



(iii), C^ f ^ fi,... „ „ average J'jc^^-height. 



For the first formula the sample stem measured must be such 



C 



that its contents = — . 

 n 



In using the second formula the height and form-factor of the 

 sample stems measured must be identical with the average height 

 and form-factor of the crop or height-and-girth class, a condi- 

 tion that is more easily realized than the equality demanded for 

 the use of the first formula. 



Of the quantities A, H, and F, the first is obtained at once by 

 direct measurement of the girths of all the stems taken at a 

 fixed height above the ground ; while the other two are ideal, and 

 must be obtained as accurately as possible by computation from 

 the measurements of the sample stems. 



In those methods of valuation survey which are based on the 

 actually measured contents of sample trees and on the measured 

 basal areas of all the trees, a fourth formula, derived from formula 

 (ii), may be substituted for formula (i). Using the same expres- 

 sions as before, aud supposing thatc, a, h, and_/, respectively are 

 the mean contents, basal area, height, and form-factor of the type 

 or sample trees, we have — 



C= A BF. Formula (ii), 



andc = a! x h X /. by assumption ; 



Hence C : c = A HF : a h f 



and as BF is by assumption = h f 



A 



:. C = e — ..,, Formula (iv). 



Formula (iv) is to be preferred to formula (i), for two reasons : 

 firstly, because the important and easily obtained term A enters 

 into it; and, secondly, because the sample stems have to furnish 

 only the average height and form-factor, not the average contents, 

 of all the trees of the crop or of the diameter-and-height class, so 



